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The current book makes several useful topics from the theory of special functions, in particular the theory of spherical harmonics and Legendre polynomials in arbitrary dimensions, available to undergraduates studying physics or mathematics. With this audience in mind, nearly all details of the calculations and proofs are written out, and extensive background material is covered before exploring the main subject matter. Contents: Introduction and Motivation; Working in p Dimensions; Orthogonal Polynomials; Spherical Harmonics in p Dimensions; Solutions to Problems. Readership: Undergraduate an

Spherical harmonics. --- Spherical functions. --- Legendre's polynomials. --- Mathematical physics. --- Physical mathematics --- Physics --- Functions, Spherical --- Spherical harmonics --- Transcendental functions --- Spheroidal functions --- Functions, Potential --- Potential functions --- Harmonic analysis --- Harmonic functions --- Polynomials, Legendre's --- Orthogonal polynomials --- Mathematics